Exposedness of elementary positive maps between matrix algebras

• URL: http://arxiv.org/abs/2301.05788v1
• Date: Fri, 13 Jan 2023 23:34:34 GMT
• Title: Exposedness of elementary positive maps between matrix algebras
• Authors: Seung-Hyeok Kye
• Abstract summary: The positive linear maps $ad_s$ which send matrices $x$ to $s*xs$ play important roles in quantum information theory as well as matrix theory. It was proved by Marciniak that the map $ad_s$ generates an exposed ray of the convex cone of all positive linear maps.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The positive linear maps $\ad_s$ which send matrices $x$ to $s^*xs$ play important roles in quantum information theory as well as matrix theory. It was proved by Marciniak [Linear Multilinear Alg. 61 (2013), 970--975] that the map $\ad_s$ generates an exposed ray of the convex cone of all positive linear maps. In this note, we provide two alternative proofs, using Choi matrices and Woronowicz's method, respectively.

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